ON FORMULATIONS OF VORTICITY SYSTEMS FOR A VISCOUS INCOMPRESSIBLE-FLOW WITH NUMERICAL APPLICATIONS

The aim of this work is to present a series of analytical and numerical results related to vorticity formulations of the systems describing the motion of an incompressible viscous fluid. A rigorous variational framework for the two-dimensional Stokes system is used as a basis in both the stream function-vorticity and the velocity-vorticity formulations. It is shown that this allows in particular a decoupled numerical solution method for the former formulation yielding optimal convergence results. On the other hand a new finite element scheme is proposed for the latter and illustrated by computer results. Finally a study on the velocity-vorticity formulation in three dimensional space is carried out.